A New Multilevel CART Algorithm for Multilevel Data with Binary Outcomes

AbstractThe multilevel logistic regression model (M-logit) is the standard model for modeling multilevel data with binary outcomes. However, many assumptions and restrictions should be considered when applying this model for unbiased estimation. To overcome these limitations, we proposed a multilevel CART (M-CART) algorithm which combines the M-logit and single level CART (S-CART) within the framework of the expectation-maximization. Simulation results showed that the proposed M-CART provided substantial improvements on classification accuracy, sensitivity, and specific over the M-logit, S-CART, and single level logistic regression model when modeling multilevel data with binary outcomes. This benefit of using M-CART was consistently found across different conditions of sample size, intra-class correlation, and when relationships between predictors and outcomes were nonlinear and nonadditive.